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The flat world vs round world argument is not really relevant to the fact that many people from Westeros know very little of what lies beyond Asshai to east, short of what a handful of travelers may have previously explored and relayed through written or verbal stories.

I've not heard of Yi-Ti mentioned at all in the show and even in the World of Ice and Fire lore book, Sothoryos is lightly touched on. Nothing east or south of Asshai or west of Westeros is common knowledge, in my opinion.

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Because it clearly isn't common knowledge that worlds are round in this story. Much like it wasn't common knowledge through real history. Some civilisations figured it out amazingly early, but others were fairly recent as the timeline of our species goes.

Quite likely Valyria had figured it out, but they're long gone.

Assuming the world is round. This is fantasy. Technically it doesn't have to be round.

Actually GRRM confirms that the world is in fact round. However, I think you are correct in assuming that it isn't like super common knowledge. That said, Arya is about as high born as you can get and had a Maester in her castle to teach her. Whether or not she is aware that the world is round I do not know, but she probably has a better chance of knowing it than a peasant girl or even the girl of a well off merchant or smith.

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The dialogue proves that Arya doesn't know what's west of Westeros. It neither proves nor disproves anything about her knowledge of the shape of the world.

In medieval times woman received no education (even in relatively modern times, highborn women received little formal education). So Arya would be as dumb as a rock when it came to geography. Her skill set would have been limited to embroidery and conversation.

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She was taught by a Septa IIRC, and her lessons covered things like needlework, which Arya hated. The Septa was one of the folk whose head ended up on spikes after Ned was beheaded. Sansa was shocked by why someone felt it necessary to do that to her.

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In medieval times woman received no education (even in relatively modern times, highborn women received little formal education). So Arya would be as dumb as a rock when it came to geography. Her skill set would have been limited to embroidery and conversation.

You seem to forget how impressed Tywin was with her knowledge of history. I'm guessing that she knows the world is round and it was a joke.

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She was taught by a Septa IIRC, and her lessons covered things like needlework, which Arya hated. The Septa was one of the folk whose head ended up on spikes after Ned was beheaded. Sansa was shocked by why someone felt it necessary to do that to her.

We know she received lessons from the Septa, yes. We also know that she knows the things that the Maester was teaching Bran, from her scenes in Harrenhall.

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What lies beyond the Sunset Sea is a mystery, and nobody that has sailed west to explore has ever returned. The reference in the books that I remember is of Brandon the Shipwright. He attempted to sail across the Sunset Sea, but was never seen again. It is known that he never visited Asshai, and his son, Brandon the burner had the remainder of the northern fleet burned in his grief.

I believe there was another reference to this subject in a legend or story among the Iron born, but I do not recall the names or of how the story went.

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I am pretty sure every civilization in history comparable to Westerosi or the Free Cities had a pretty good idea about the shape of the earth.

Astronomy is a quite common field of study for measters, it would be very odd if they hadn't figured that out by now. And IIRC, Luwin in Winterfell was particularly into it.

So whatever the shape of this world is, Arya is most likely educated on it, even if it is not "common knowledge".

I agree with this, and don't feel like a retort of "your mistaken" is a very convincing argument to show otherwise. I think the Maesters definitely know that the planet is round, and I don't think this would be such top secret or complicated information that the general populous that are not Maesters wouldn't be aware of this. I think It's very likely that Arya knows that the world is round.

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I believe there was another reference to this subject in a legend or story among the Iron born, but I do not recall the names or of how the story went.

Here it is, from the Kingsmoot:

Quote

Aeron knew some Farwynds, a queer folk who held lands on the westernmost shores of Great Wyk and the scattered isles beyond, rocks so small that most could support but a single household. Of those, the Lonely Light was the most distant, eight days' sail to the northwest amongst rookeries of seals and sea lions and the boundless grey oceans. The Farwynds there were even queerer than the rest. Some said they were skinchangers, unholy creatures who could take on the forms of sea lions, walruses, even spotted whales, the wolves of the wild sea.

Lord Gylbert began to speak. He told of a wondrous land beyond the Sunset Sea, a land without winter or want, where death had no dominion. "Make me your king and I shall lead you there," he cried. "We will build ten thousand ships as Nymeria once did and take sail with all our people to the land beyond the sunset. There every man shall be a king and every wife a queen."

His eyes, Aeron saw, were now grey, now blue, as changeable as the seas. Mad eyes, he thought, fool's eyes. The vision he spoke of was doubtless a snare of the Storm God to lead the Ironborn to destruction.